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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN-EP-2001-06620 September 2001

Search for Single Top QuarkProduction at LEP2

The OPAL Collaboration

Abstract

A search for single top quark production via flavour changing neutral currents (FCNC) wasperformed with data collected by the OPAL detector at the e+e− collider LEP. Approxi-mately 600 pb−1 of data collected at

√s = 189 - 209GeV were used to search for the FCNC

process e+e− → tc(u) → bWc(u). This analysis is sensitive to the leptonic and the hadronicdecay modes of the W boson. No evidence for a FCNC process is observed. Upper limitsat the 95% confidence level on the single top production cross-section as a function of thecentre-of-mass energy are derived. Limits on the anomalous coupling parameters κγ and κZ

are determined from these results.

(Submitted to Physics Letters B)

The OPAL Collaboration

G.Abbiendi2, C.Ainsley5, P.F. Akesson3, G.Alexander22, J. Allison16, G.Anagnostou1,K.J.Anderson9, S.Arcelli17, S.Asai23, D.Axen27, G.Azuelos18,a, I. Bailey26, E. Barberio8,R.J. Barlow16, R.J. Batley5, T.Behnke25, K.W.Bell20, P.J. Bell1, G.Bella22, A.Bellerive6,G.Benelli4, S. Bethke32, O.Biebel32, I.J. Bloodworth1, O.Boeriu10, P. Bock11, J. Bohme25,

D.Bonacorsi2, M.Boutemeur31, S. Braibant8, L. Brigliadori2, R.M.Brown20,H.J. Burckhart8, J. Cammin3, R.K.Carnegie6, B.Caron28, A.A.Carter13, J.R.Carter5,C.Y.Chang17, D.G.Charlton1,b, P.E.L.Clarke15, E.Clay15, I. Cohen22, J. Couchman15,

A.Csilling8,i, M.Cuffiani2, S.Dado21, G.M.Dallavalle2, S.Dallison16, A.De Roeck8, E.A.DeWolf8, P.Dervan15, K.Desch25, B.Dienes30, M.S.Dixit6,a, M.Donkers6, J.Dubbert31,

E.Duchovni24, G.Duckeck31, I.P.Duerdoth16, E. Etzion22, F. Fabbri2, L. Feld10, P. Ferrari12,F. Fiedler8, I. Fleck10, M.Ford5, A. Frey8, A. Furtjes8, D.I. Futyan16, P.Gagnon12,

J.W.Gary4, G.Gaycken25, C.Geich-Gimbel3, G.Giacomelli2, P.Giacomelli2, D.Glenzinski9,J.Goldberg21, K.Graham26, E.Gross24, J.Grunhaus22, M.Gruwe8, P.O.Gunther3,

A.Gupta9, C.Hajdu29, M.Hamann25, G.G.Hanson12, K.Harder25, A.Harel21,M.Harin-Dirac4, M.Hauschild8, J. Hauschildt25, C.M.Hawkes1, R.Hawkings8,

R.J.Hemingway6, C.Hensel25, G.Herten10, R.D.Heuer25, J.C.Hill5, K.Hoffman9,R.J.Homer1, D.Horvath29,c, K.R.Hossain28, R.Howard27, P.Huntemeyer25,

P. Igo-Kemenes11, K. Ishii23, A. Jawahery17, H. Jeremie18, C.R. Jones5, P. Jovanovic1,T.R. Junk6, N.Kanaya26, J.Kanzaki23, G.Karapetian18, D.Karlen6, V.Kartvelishvili16,

K.Kawagoe23, T.Kawamoto23, R.K.Keeler26, R.G.Kellogg17, B.W.Kennedy20, D.H.Kim19,K.Klein11, A.Klier24, S.Kluth32, T.Kobayashi23, M.Kobel3, T.P.Kokott3, S.Komamiya23,

R.V.Kowalewski26, T.Kramer25, T.Kress4, P.Krieger6, J. von Krogh11, D.Krop12,T.Kuhl3, M.Kupper24, P.Kyberd13, G.D. Lafferty16, H. Landsman21, D. Lanske14,

I. Lawson26, J.G. Layter4, A. Leins31, D. Lellouch24, J. Letts12, L. Levinson24, J. Lillich10,C. Littlewood5, S.L. Lloyd13, F.K. Loebinger16, G.D. Long26, M.J. Losty6,a, J. Lu27,

J. Ludwig10, A.Macchiolo18, A.Macpherson28,l, W.Mader3, S.Marcellini2, T.E.Marchant16,A.J.Martin13, J.P.Martin18, G.Martinez17, G.Masetti2, T.Mashimo23, P.Mattig24,W.J.McDonald28, J.McKenna27, T.J.McMahon1, R.A.McPherson26, F.Meijers8,

P.Mendez-Lorenzo31, W.Menges25, F.S.Merritt9, H.Mes6,a, A.Michelini2, S.Mihara23,G.Mikenberg24, D.J.Miller15, S.Moed21, W.Mohr10, T.Mori23, A.Mutter10, K.Nagai13,

I. Nakamura23, H.A.Neal33, R.Nisius8, S.W.O’Neale1, A.Oh8, A.Okpara11, M.J.Oreglia9,S.Orito23, C. Pahl32, G. Pasztor8,i, J.R.Pater16, G.N.Patrick20, J.E. Pilcher9, J. Pinfold28,

D.E.Plane8, B. Poli2, J. Polok8, O. Pooth8, A.Quadt3, K.Rabbertz8, C.Rembser8,P.Renkel24, H.Rick4, N.Rodning28, J.M.Roney26, S. Rosati3, K.Roscoe16, Y.Rozen21,

K.Runge10, D.R.Rust12, K. Sachs6, T. Saeki23, O. Sahr31, E.K.G. Sarkisyan8,m, C. Sbarra26,A.D. Schaile31, O. Schaile31, P. Scharff-Hansen8, M. Schroder8, M. Schumacher25,

C. Schwick8 , W.G. Scott20, R. Seuster14,g , T.G. Shears8,j , B.C. Shen4,C.H. Shepherd-Themistocleous5 , P. Sherwood15, A. Skuja17, A.M. Smith8, G.A. Snow17,R. Sobie26, S. Soldner-Rembold10,e, S. Spagnolo20, F. Spano9, M. Sproston20, A. Stahl3,

K. Stephens16, D. Strom19, R. Strohmer31, L. Stumpf26, B. Surrow25, S. Tarem21,M.Tasevsky8, R.J.Taylor15, R.Teuscher9, J. Thomas15, M.A.Thomson5, E.Torrence19,

D.Toya23, T.Trefzger31, A.Tricoli2, I. Trigger8, Z. Trocsanyi30,f , E.Tsur22,

1

M.F.Turner-Watson1, I. Ueda23, B.Ujvari30,f , B.Vachon26, C.F.Vollmer31, P.Vannerem10,M.Verzocchi17, H.Voss8, J. Vossebeld8, D.Waller6, C.P.Ward5, D.R.Ward5, P.M.Watkins1,

A.T.Watson1, N.K.Watson1, P.S.Wells8, T.Wengler8, N.Wermes3, D.Wetterling11

G.W.Wilson16, J.A.Wilson1, T.R.Wyatt16, S.Yamashita23, V. Zacek18, D. Zer-Zion8,k

1School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK2Dipartimento di Fisica dell’ Universita di Bologna and INFN, I-40126 Bologna, Italy3Physikalisches Institut, Universitat Bonn, D-53115 Bonn, Germany4Department of Physics, University of California, Riverside CA 92521, USA5Cavendish Laboratory, Cambridge CB3 0HE, UK6Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa,Ontario K1S 5B6, Canada8CERN, European Organisation for Nuclear Research, CH-1211 Geneva 23, Switzerland9Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago IL 60637,USA10Fakultat fur Physik, Albert Ludwigs Universitat, D-79104 Freiburg, Germany11Physikalisches Institut, Universitat Heidelberg, D-69120 Heidelberg, Germany12Indiana University, Department of Physics, Swain Hall West 117, Bloomington IN 47405,USA13Queen Mary and Westfield College, University of London, London E1 4NS, UK14Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germany15University College London, London WC1E 6BT, UK16Department of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UK17Department of Physics, University of Maryland, College Park, MD 20742, USA18Laboratoire de Physique Nucleaire, Universite de Montreal, Montreal, Quebec H3C 3J7,Canada19University of Oregon, Department of Physics, Eugene OR 97403, USA20CLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK21Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel22Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel23International Centre for Elementary Particle Physics and Department of Physics, Univer-sity of Tokyo, Tokyo 113-0033, and Kobe University, Kobe 657-8501, Japan24Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel25Universitat Hamburg/DESY, II Institut fur Experimental Physik, Notkestrasse 85, D-22607 Hamburg, Germany26University of Victoria, Department of Physics, P O Box 3055, Victoria BC V8W 3P6,Canada27University of British Columbia, Department of Physics, Vancouver BC V6T 1Z1, Canada28University of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canada29Research Institute for Particle and Nuclear Physics, H-1525 Budapest, P O Box 49, Hun-gary30Institute of Nuclear Research, H-4001 Debrecen, P O Box 51, Hungary31Ludwigs-Maximilians-Universitat Munchen, Sektion Physik, Am Coulombwall 1, D-85748

2

Garching, Germany32Max-Planck-Institute fur Physik, Fohring Ring 6, 80805 Munchen, Germany33Yale University,Department of Physics,New Haven, CT 06520, USA

a and at TRIUMF, Vancouver, Canada V6T 2A3b and Royal Society University Research Fellowc and Institute of Nuclear Research, Debrecen, Hungarye and Heisenberg Fellowf and Department of Experimental Physics, Lajos Kossuth University, Debrecen, Hungaryg and MPI Muncheni and Research Institute for Particle and Nuclear Physics, Budapest, Hungaryj now at University of Liverpool, Dept of Physics, Liverpool L69 3BX, UKk and University of California, Riverside, High Energy Physics Group, CA 92521, USAl and CERN, EP Div, 1211 Geneva 23m and Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel.

3

1 Introduction

In the mid 1990’s, the LEP collider at CERN entered a new phase of operation, LEP2,with the first e+e− collisions above the W+W− threshold. Between 1998 and 2000, with theinstallation of additional super-conducting radio-frequency accelerating cavities, the centre-of-mass energy of the LEP collider was further increased. The LEP2 data accumulatedat centre-of-mass energies between 189GeV and 209GeV have opened up a new kinematicdomain for particle searches.

The top quark mass was measured at the Tevatron collider to be 174.3 ± 5.1GeV/c2 [1, 2].Due to this high mass, top quarks may only be singly produced at LEP2. Single top quarkproduction in the Standard Model (SM) process e+e− → e−νetb has a cross-section of about10−4 fb at LEP2 energies [3] and can not be seen with the available luminosities. Anotherpossible process for single top quark production is the flavour changing neutral current(FCNC) reaction1:

e+e− → tc(u). (1)

Such FCNC are known to be absent at the tree level in the SM but can naturally appearat the one-loop level due to CKM mixing which leads to cross-sections of the order of 10−9 fbat LEP2 energies [4]. Extensions of the SM such as supersymmetry, exotic quarks, andmulti-Higgs doublet models could lead to an enhancement of such transitions [5, 6, 7, 8].In this paper the search for single top production via the FCNC reaction e+e− → tc(u) isreported.

At the Tevatron, the CDF Collaboration performed a search for FCNC in the top de-cays t → γ c(u) and t → Z c(u) in pp collisions at a centre-of-mass energy of 1.8TeV. Theyobtained upper limits at the 95% confidence level (CL) on the branching fractions [9]:Br(t → cγ) + Br(t → uγ) < 3.2% and Br(t → cZ) + Br(t → uZ) < 33%.

The FCNC reaction can be described with the parameters κγ and κZ which representthe tree-level γ and Z exchange contributions to e+e− → tc(u). Thus, the Born-level cross-section for single top production in e+e− collisions for

√s > mt can be written as [6]:

σ[e+e− → tc(u)] =πα2

s

(

1 − m2t

s

)2[

κ2γe

2q

s

m2t

(

1 +2m2

t

s

)

+κ2

Z(1 + a2w)(2 +

m2

t

s)

4 sin4 2ϑW(1 − m2

Z

s)2

+ 3κγκZaweq

sin2 2ϑW(1 − m2

Z

s)

]

, (2)

where s is the centre-of-mass energy squared, α is the fine structure constant, eq = 2/3 andmt are the charge and mass of the top quark, mZ is the Z boson mass, and aw = 1−4 sin2 ϑW

with ϑW being the weak-mixing angle. The three terms in Equation 2 correspond to thecontribution from annihilation via a photon, a Z boson, and their interference. Using thepublished limits of CDF on FCNC, one can derive the following model-dependent limits at95% CL [6, 9]: κ2

γ < 0.176 and κ2Z < 0.533.

1Throughout this paper, charge conjugate states are implied.

4

In principle, a large FCNC coupling could not only lead to the associated production ofa top plus a light quark at LEP2, but also to sizable branching ratios of the top quark intoγc(u) or Zc(u). This analysis uses only the t → bW channel. The reduction of the branchingratio BR(t → bW) due to possible FCNC decays is taken into account in the results section.

2 Data and Monte Carlo Samples

The present analysis is based on data collected by the OPAL detector [10] from 1998 to 2000at centre-of-mass energies between 189GeV and 209GeV. OPAL is a multipurpose highenergy physics detector incorporating excellent charged and neutral particle detection andmeasurement capabilities. The search presented here uses 600.1 pb−1 of data collected athigh energies for which the necessary detector components were required to be operationalwhile the data were recorded. In addition, 11.3 pb−1 of calibration data were collected at√

s ∼ mZ in 1998–2000 and have been used for fine tuning of the Monte Carlo simulation. Inthis paper, the data sample recorded in 1998 at

√s ≃ 189GeV is analysed in one bin, while

the data from 1999 are divided into four samples at√

s ≃ 192, 196, 200 and 202GeV. Thedata collected in 2000 is analysed in two samples of mean centre-of-mass energies of about205 and 207GeV.

A variety of Monte Carlo samples were generated for the evaluation of the detectionefficiencies for single top production and SM background processes. In all samples, thehadronisation process is simulated with JETSET 7.4 [11] with parameters described in Refer-ence [12] and the W boson mass is set to mW = 80.33GeV/c2. For each Monte Carlo sample,the detector response to the generated particles is simulated by a GEANT3 based package [13].

The main Monte Carlo generator used for the description of our signal is PYTHIA [11],which produces tc(u) via an s-channel exchange of a Z boson. The top quark decays into ab quark and a W boson before it can form a bound state or radiate gluons. A colour stringis formed between the b and c(u) quarks to form a colour singlet. All couplings and quarkfragmentation parameters for e+e− → tc(u) are set as in Z decays to quark pairs. For anevaluation of systematic errors associated with the Monte Carlo modelling, the signal is alsomodelled with a different PYTHIA process and the EXOTIC generator [14]. This other PYTHIAprocess is based on a model [15] for the production of a horizontal gauge boson, calledR0, with the decay R0 → tc(u). The EXOTIC generator was developed for pair or singleproduction of heavy and excited fermions. Here, the top quark is the heavy fermion and itsproduction is associated with a c or u quark. A sequential decay model is assumed with allcouplings to the known gauge bosons set to the SM expectations. For all three generators,samples for three different top quark masses (169, 174, and 179GeV/c2) have been generated.The signal Monte Carlo samples used for the reaction e+e− → tc(u) encompass a wide rangeof schemes for the form of the FCNC couplings, the angular distributions of the final stateparticles, and the parton shower parameters.

The background processes are simulated, with more statistics than the data collected,using the following event generators: PYTHIA, KK2F [16], and HERWIG [17] for (Z/γ)∗→ qq(γ);grc4f [18], KORALW [19], and EXCALIBUR [20] for four-fermion (4f) processes; and HERWIG,PHOJET [21], and Vermaseren [22] for two-photon scattering.

5

3 Event Selection

The searches for single top events e+e− → tc(u) → bWc(u) are sensitive to the leptonic andhadronic decays of the W boson: W → ℓνℓ and W → qq. The leptonic channel is a cleanfinal state with specific topology and kinematics; it is characterised by two hadronic jets,one isolated lepton, some missing energy (carried away by the neutrino), and the presenceof a b-hadron decay. While the hadronic channel is not as clean as the leptonic channel,it is statistically significant because BR(W → hadron) ≈ 68% and BR(W → ℓνℓ) ≈ 32%(ℓ = e, µ, and τ). The hadronic channel is characterised by four hadronic jets with specifictopology and kinematics, large visible energy, and the presence of a b-hadron decay. Commonsearch procedures are applied to both channels. The event selection begins with loose globalpreselection criteria designed to remove most of the two-photon and low multiplicity events.To obtain optimal resolution for single top candidates, kinematic fits are performed to rejectbadly reconstructed events and background which are not compatible with the topologyof single top events. Consequently, the event selection is followed by detailed preselectioncuts for both the leptonic and the hadronic channels. The final candidate events are thenidentified using relative likelihood functions. Each step will be described briefly in thefollowing subsections.

3.1 Global Event Selection Criteria

Events are reconstructed from tracks in the central tracking system and energy clusters inthe electromagnetic and hadron calorimeters, using selection criteria which are the same asthose used for the OPAL Higgs analysis [23]. Because of the presence of jets in a singletop event, general multi-hadronic preselections are applied. Each event must qualify as amulti-hadronic final state according to the criteria of References [24, 25]. These cuts removeevents with low multiplicity or little visible energy and reject effectively two-photon and pureleptonic events.

The final state particles and clusters are grouped into jets using the Durham algo-rithm [26]. These jets are used as reference jets in the following assignment procedure.In calculating the visible energies and momenta, Evis and ~pvis, of the event and of individualjets, corrections are applied to prevent double-counting of the energy of the tracks and theirassociated clusters [27].

3.2 Lepton Identification

Lepton identification for the leptonic channel relies primarily on the isolation criteria ofa prompt charged particle. Isolated leptons are identified using the Neural Network (NNℓ)described in Reference [28]. The NNℓ uses all tracks in an event with |~p| > 2 GeV/c which areconsidered one-by-one in decreasing order of momentum. They are used as seed tracks andall tracks and unassociated clusters within 10◦ of the seed track define the lepton. Afterwardthe leptons are classified as one-prong or three-prong candidates depending on the numberof tracks within the 10◦ cone. Around the seed candidate an annular cone of 30◦ is drawnconcentric with and excluding the 10◦ narrow cone. This serves to define the isolation criteriaof the lepton candidate. The NNℓ provides a distinctive signature for high energy leptons

6

from the particle flow in the annular and narrow cones. However, this procedure is flavourblind; the main interest is to retain high identification efficiency. Thus, the NNℓ topologicalidentification is sensitive to the detection of electrons, muons, and taus with efficiencies of84%, 84%, and 75%, respectively. The probability of misidentifying a hadron from a partonshower as a lepton is around 1% for NNℓ > 0.75. The main source of misidentified leptonscomes from low-multiplicity gluon jets.

The lepton with the largest NNℓ output in every event is taken to be the lepton of thet → bW → b ℓνℓ decay. In order to improve the performance of the kinematic fits, a simpleidentification is used to determine the mass (flavour) of the lepton candidate. First, all three-prong candidates are classified as taus. Then, a lepton is classified as an electron if Pe ≥ 0.5,Eℓ > 20GeV, and cos θℓ−ν < 0.25, where Pe is the standard OPAL electron identificationprobability [29], Eℓ is the energy of the lepton, and θℓ−ν is the opening angle between thelepton and the missing momentum vector. Of the remaining leptons, the candidates withPe < 0.5, Eℓ > 20GeV, and cos θℓ−ν < 0.25 are classified as muons, while the others arelabelled as taus.

3.3 Event Kinematics

At a centre-of-mass energy of√

s ≈ 189 GeV the top quark is produced close to threshold.As the top quark is nearly at rest, the W boson in the e+e− → tc(u) → bWc(u) reaction hasalmost constant energy EW ≃ (m2

t + m2W − m2

b)/2 mt, which also leads to fixed energy forthe b quark Eb ≃ (m2

t −m2W +m2

b)/2 mt. With increasing centre-of-mass energy this uniquekinematic signature gets diluted.

These specific kinematic properties are exploited by using kinematic fits. First, the eventis constrained to pass a 4C kinematic fit which ensures that the energy and momentum areconserved2. The 4C kinematic fit is employed to remove badly reconstructed events andevents with missing particles along the beam pipe. The χ2 probability of the 4C fit is thusrequired to be larger than 10−5.

To obtain optimal resolution for the reconstructed candidates and performance for thejet assignment, we use additional kinematic fits which enforce energy and momentum con-servation and impose the appropriate mass constraints. These fits are referred to as the 6Cfits with the tc(u) or the WW hypothesis:

• e+e− → tc(u) → bWc(u): W boson and top quark invariant mass constraints.

• e+e− →WW: two W boson invariant mass constraints.

In the 6C kinematic fits the W mass and the top quark mass are fitted with a softconstraint, approximating the Breit-Wigner shapes by Gaussian resolution functions. As forthe 4C fit, we still refer any mass constrained fit as a 6C fit for b ℓνℓ c(u) events. To ensurethat the kinematic properties of the event candidates match our signal process, we requireP(6C) > 10−5 for the tc(u) 6C fit.

2For semileptonic events, there are three unmeasured variables corresponding to the neutrino momentum

so that the effective number of constraints in the leptonic mode is one. Nevertheless, any fit which implies

that energy and momentum are conserved for both the leptonic and hadronic channels will be referred to as

a 4C fit.

7

3.4 B-Tagging

The dominant background in this analysis comes from WW events. In e+e− →WW events,the only heavy quark commonly produced is the charm quark. The production of bottomquarks is highly suppressed due to the small magnitude of |Vub| and |Vcb| and the large massof the top quark. Furthermore, since the top quark is expected to decay into a bW pair, thetagging of jets originating from b quarks plays an important role in single top productionsearches. The jet-wise b-tagging algorithm, which has been developed for the Higgs bosonsearch, uses three independent b-tagging methods: (1) lifetime tag, (2) high-pT lepton tag,and (3) jet shape tag. These three methods are combined using an unbinned likelihoodmethod to form a single discriminating variable for each jet [28]. The b-tag becomes im-portant for higher centre-of-mass energies because the kinematic situation changes and thesignal is less well separated from the WW background.

3.5 Jet Assignment

In the hadronic channel, the correct assignment of particles to jets plays an essential role inreducing four-jet like backgrounds. There are twelve possible combinations to assign two jetsto the W boson, the third jet to the b quark, and the fourth jet to the light flavoured quark.Therefore a discriminating variable is calculated, which is a combination of the 6C kinematicfit probability and the b-tag variable, in order to find the best matching combination to thesignal hypothesis. The 6C fit helps to identify the two jets coming from the W and to findthe third jet which matches kinematically to form the invariant top quark mass. In additionthe b-tag variable helps to identify if this latter jet is a b-jet. The jet assignment whichyields the largest P(b-tag, 6C) is used to choose the jet/quark assignment. P(b-tag, 6C) iscalculated as:

P(b-tag, 6C) =P(6C)P(b-tag)

P(6C)P(b-tag) + [1 − P(6C)] [1 − P(b-tag)],

where P(b-tag) is the b-tag variable and P(6C) is the probability from the tc(u) 6C fit.In the leptonic channel, the correct jet/quark assignment plays an important role in

reducing signal-like background topology. In e+e− → tc(u) → b ℓνℓ c(u), there are only twopossible jet assignments. One of the jets must come from the hadronisation of the b quarkand the other from the light flavoured quark. The bottom jet is taken to be the one withthe largest P(b-tag, 6C) from the tc(u) 6C fit.

With the jet assignment method described here, a Monte Carlo study shows that therate of correct b-jet (non b-jet) assignment at

√s = 189GeV is about 96% (94%) and 84%

(73%) for the leptonic and hadronic channels, respectively.

3.6 Single Top Candidate Preselection

To help further reduce the background after the global event selections, the kinematic fits,the b-tagging, and the jet assignment, individual preselection criteria are enforced for boththe leptonic and the hadronic channels.

8

3.6.1 Preselection: Leptonic Channel

The following preselection cuts are applied in order to reduce background with a differenttopology to our signal process:

1. Nlepton ≥ 1, where Nlepton is the number of lepton candidates as described in Section 3.2.

2. | cos θmiss| < 0.9, where | cos θmiss| is the cosine of the polar angle of the missing mo-mentum vector. This cut rejects a large portion of the qq(γ) background.

3. Mvis/√

s > 0.20, where Mvis is the invariant mass calculated from the visible energyEvis and the visible momentum ~pvis of the event.

4. |~pmiss|/√

s < 0.50, where ~pmiss is calculated from the visible momentum (~pmiss = −~pvis).This cut reject events with large missing momentum, such as qq(γ) background whenthe photon escapes detection.

5. 0.20 <∑ |~pT|/

√s < 0.90, where

∑ |~pT| is the scalar sum of the transverse momentumcomponents for all the good tracks and unassociated clusters. This cut prevents thevisible momentum being toward the beam direction and rejects non-radiative qq eventswith no missing energy.

6. NNℓ > 0.75, where NNℓ is the primary lepton Neural Network output as described inSection 3.2.

After the preselection the background is well described by 4f and qq events. Other finalstates, such as two-photon events, are negligible. The main background (around 95%) is dueto WW → qqℓνℓ events. The fraction of events with four quarks in the final state selectedwith the leptonic preselection criteria is negligible.

3.6.2 Preselection: Hadronic Channel

The following preselection cuts are applied in order to select only four-jet like events:

1. The event must contain at least 15 charged tracks.

2. The maximum energy of any electron or muon found in the event (identified as de-scribed in Reference [30]) must be less than 40GeV.

3. The radiative process e+e−→ (Z/γ)∗γ→ qqγ is reduced by requiring that the effectivecentre-of-mass energy

√s ′ [25] be at least 150GeV.

4. The Durham jet resolution parameter y34, at which the number of jets changes fromthree to four, is required to be larger than 0.001.

5. The (Z/γ)∗→ qq background is further suppressed by requiring that the event shapeparameter C [31], which is close to one for spherical events, is larger than 0.4.

After the preselection the background is well described by 4f and qq events. The expectedbackground is composed of 41% (70%) of 4f and 59% (30%) of qq processes at

√s ≃ 189

(207)GeV. Other final states, such as two-photon events, are negligible. The fraction ofqqℓνℓ events selected by the hadronic preselection criteria is less than 1%.

9

3.7 Likelihood Selection

The final separation of the signal from the background is achieved with a conventional multi-variable relative likelihood function [32]:

L =Psignal

Psignal + Pbackground, with P =

∏

i

pi.

The template (or reference) histograms of the input variables, pi, are used as the probabilitydensity functions for the calculation of Psignal and Pbackground. We rely on Monte Carlo eventsto compute the probability density functions.

3.7.1 Likelihood: Leptonic Channel

For each event satisfying the qqℓνℓ preselection cuts, a binned likelihood function is con-structed, with one class for the signal and one for the 4f background. The relative likelihoodis calculated using the following variables:

Ec(u): The energy of the light flavoured jet.

M4Cqq

: The invariant mass of the qq system after the 4C fit.

Mℓν =√

E2beam − (~p 4C

ℓν)2: Pseudo mass of the ℓνℓ system after the 4C fit, calculated from

the beam energy and the momentum of the ℓνℓ pair.

ln y12: The logarithm of the Durham jet resolution parameter at which the number ofreconstructed jets passes from one to two.

M6Cqq

+ M6Cℓν

: The sum of the di-jet and ℓνℓ invariant masses for the 6C fit under the WWhypothesis.

b-tag: The b-tag variable of the selected bottom jet.

P(b-tag, 6C): The discriminant variable which combines the b-tag variable and the tc(u)6C fit probability.

Jets tagged as light flavoured jets in the background from SM processes have much highervalues of Ec(u). The second and third variables offer good discrimination for WW → qqℓνℓ

events since they exploit the specific angular distribution of signal events. The variable y12

exploits the unique jet distribution in tc(u) events. To further remove the background fromsemileptonic WW decays, we use M6C

qq + M6Cℓν . Finally, we use the b-tag variable and the

P(b-tag, 6C) of the b-jet to separate bottom-less events. Figure 1 shows the distributionsof the input variables for data, the SM background, and the simulated single top signal at√

s = 189GeV. There is good agreement between data and Monte Carlo distributions frombackground processes.

10

3.7.2 Likelihood: Hadronic Channel

For each event satisfying the qqqq preselection cuts, a binned likelihood function is con-structed, with one class for the signal and two for the qqqq and the qq backgrounds. Therelative likelihood is calculated using the following variables:

χ2(6C fit): The χ2 of the tc(u) 6C kinematic fit.

Ec(u)/Evis: The ratio of the energy of the c(u) jet and the total visible energy.

Thrust: The value of the thrust for the event [11].

b-tag: The b-tag variable of the selected bottom jet.

cos( 6 (~pWq1, ~pWq2)): The cosine of the angle between the two jets tagged as decay productsof the W boson.

The thrust variable exploits the different event topologies between signal and back-grounds. The b-tag variable is used as an effective likelihood input because the top quark isexpected to decay into a b quark. The other three variables exploit the specific kinematicsof signal events. Figure 2 shows the distributions of the input variables for data, the SMbackground, and the simulated single top signal at

√s = 189GeV. There is good agreement

between data and Monte Carlo distributions from background processes.

3.7.3 Likelihood: Both Channels

In Figure 3 the relative likelihood functions for the leptonic and hadronic channels are shownfor data collected at

√s ≃ 205 - 207GeV and for the SM expectation. No excess of events

is observed. The likelihood functions for FCNC signal events for an assumed arbitrarycross-section of 3 pb are also depicted in Figure 3. It can be seen that the expected signalcontribution is concentrated at high values of L.

There is no evidence of single top quark production in the data for any√

s. Thus, thefinal likelihood cuts are chosen at each value of

√s so as to minimise the expected upper

limit on the signal cross-section and thus to maximise the expected exclusion sensitivity. Thenumber of selected data and expected SM background events as a function of the centre-of-mass energies are shown in Table 1.

4 Systematic Errors

4.1 Signal Efficiencies and SM Backgrounds

Sources of systematic uncertainties are investigated for their effect on the signal detectionefficiencies and the SM backgrounds. They are listed in Table 2 for three of the energy binsand are discussed below. All checks were performed for all centre-of-mass energies. Possiblecolor reconnection and Bose-Einstein effects were not investigated.

The errors on the background and signal rates from the modelling of the preselectionvariables and of the detector response are a few percent. These uncertainties are evaluated

11

Label√

s Lumi. Leptonic Channel Hadronic Channel(GeV) (GeV) (pb−1) Data SM Total Data SM Total

189 188.7 172.1 3 4.0 13 11.6192 191.6 28.9 0 1.0 7 5.1196 195.6 74.8 1 2.9 6 6.4200 199.6 77.2 3 2.7 10 9.4202 201.6 36.1 2 1.2 8 7.5205 205.1 80.3 1 2.0 11 10.1207 206.8 130.8 6 3.8 14 16.4

Table 1: The luminosity-weighted mean centre-of-mass energies, the integrated luminosities,the number of selected data and expected SM background events at

√s = 189 - 209GeV are

shown for the leptonic and hadronic channels.

based on comparisons of the distributions of the variables in the calibration data collectedat

√s ∼ mZ and the Monte Carlo simulation. The effects of detector mis-calibration and

deficiencies were investigated by varying the jet and lepton energy scales over a reasonablerange [33]. The uncertainties on the energy resolution and the angular resolution werealso evaluated, but have much smaller effects. A comparison of alternative Monte Carlogenerators for the background accounts for an additional uncertainty on the backgroundrates. The difference between the luminosity-weighted centre-of-mass energies in data andthe value of

√s used in the main Monte Carlo samples results in an additional uncertainty

on the background and signal selection efficiencies due to the use of an energy constraint inthe kinematic fits. Lepton identification accounts for an extra uncertainty for the leptonicchannel.

One of the dominant errors in both analysis channels arises from the b-tagging. Recentimprovements in the knowledge of heavy quark production processes and decays, such as theb-hadron charged decay multiplicity and the gluon splitting rate to heavy quarks, are takeninto account in the analysis by reweighting Monte Carlo events [34]. The sensitivity to theb-vertex reconstruction was assessed by degrading or improving the tracking resolution inthe Monte Carlo. It was found that changing the track parameter resolutions by ±5% in theMonte Carlo simulation covers the range of possible differences between data and simulatedevents. Overall it leads to an uncertainty of 3.8-8.4% for the b-tag rates of backgroundand signal events. The finite size of the Monte Carlo samples used in this analysis resultsin an additional uncertainty of a few percent for the background and the signal selectionefficiencies.

All the different systematic effects for the background and the signal efficiencies aretreated as being independent. The total uncertainties on the background and signal rates,for both the leptonic and the hadronic channel, are in the same range and show smalldependencies on the centre-of-mass energy. For each centre-of-mass energy, the systematicerrors are included in the calculation of the cross-section upper limits.

12

Source of Leptonic Channel Hadronic ChannelSystematic Error ∆efficiency ∆background ∆efficiency ∆background

Preselection 1.0/1.4/1.2 2.0/2.2/1.9 1.0/0.4/0.3 3.2/1.4/0.5Detector Response 1.0/2.2/3.4 1.4/1.7/1.2 0.6/2.0/1.5 1.0/1.0/3.0

Background - / - / - 6.8/7.4/6.9 - / - / - 5.0/5.0/5.0√s in MC 1.1/2.4/1.9 2.7/2.1/2.3 0.6/0.8/0.5 1.5/1.3/1.4

Lepton ID 4.4/5.0/4.8 3.0/4.0/3.5 - / - / - - / - / -b-tagging 4.2/6.6/5.2 7.8/5.6/7.0 3.8/5.3/5.2 6.9/5.5/8.4

MC Statistic 2.2/2.3/2.1 1.5/2.0/1.6 2.0/1.8/1.8 5.4/5.0/4.8FCNC modelling 7.2/8.3/3.5 - / - / - 7.9/6.6/5.0 - / - / -

Total 9.8/12.5/9.1 11.5/10.9/11.0 9.1/8.9/7.6 10.7/9.2/11.4

Table 2: The relative systematic errors (in %) on the signal reconstruction efficiency andon the background modelling for

√s = 189/200/207GeV.

4.2 FCNC Modelling

Several methods of producing FCNC can be compared. A comparison of the results obtainedwith the EXOTIC and the PYTHIA samples described in Section 2 allows an estimate of theuncertainty due to the model used for the signal process. The difference is taken as amodelling uncertainty on the simulation of signal events. It is summarised in Table 2.The main disparities between all the generator schemes are the angular distributions of theparticles produced in the final state and the parton shower modelling of the initial quarks.This latter effect gives rise to one of the largest uncertainties on the signal reconstructionefficiency.

4.3 Top Quark Mass

The largest systematic uncertainty comes from the sensitivity of the event selection to theassumed value of the top quark mass. In the analysis we assume the mass of the top quarkto be 174GeV/c2. To take this dependency into account, the variation of the reconstructionefficiency is investigated using Monte Carlo events with mt= 169 and 179GeV/c2 incor-porating the experimental systematic and the FCNC model uncertainties described in theprevious sections. The dependence of the reconstruction efficiencies on the top quark massfor the leptonic and hadronic channels is summarised in Table 3.

5 Results

No evidence for single top quark production is observed in e+e− collisions at centre-of-massenergies between 189-209GeV. Limits on the single top cross-section have been derived atthe 95% CL from the measurements of the number of observed events, the reconstructionefficiencies, and the integrated luminosities [35]. The upper limit calculations for each in-dividual centre-of-mass energy are summarised in Table 3. Those results include both the

13

√s mt = 169GeV/c2 mt = 174GeV/c2 mt = 179GeV/c2

(GeV) ǫℓ ǫq σobs.95 ǫℓ ǫq σobs.

95 ǫℓ ǫq σobs.95

189 7.5 10.3 0.30 9.1 12.8 0.24 6.1 10.0 0.33192 7.5 15.3 0.99 9.5 18.0 0.81 6.9 14.9 1.04196 7.1 12.8 0.39 8.7 14.7 0.33 7.2 12.1 0.40200 7.1 14.7 0.55 8.0 16.0 0.50 7.0 15.1 0.55202 6.6 17.7 1.00 7.5 18.6 0.93 6.9 17.3 1.00205 5.9 14.4 0.48 7.0 15.7 0.43 6.2 13.9 0.49207 5.8 12.8 0.47 6.7 15.4 0.40 6.1 13.6 0.45

Table 3: The reconstruction efficiencies for the leptonic (ǫℓ) and the hadronic (ǫq) channelsare shown. The overall measured 95% CL upper limits on single top production cross-section (σobs.

95 ) are reported. The statistical and systematic uncertainties are included in thecalculation of the upper limits. The efficiencies (in %) and the limits on the cross-section (inpb) are shown as a function of the centre-of-mass energy for mt = 169, 174, and 179GeV/c2.These results assume a 100% branching fraction of the top quark into bW.

statistical and systematic errors and are valid under the assumption that mt = 169, 174,and 179GeV/c2 and that BR(t → b W) = 100%. The CDF limits constrain the t → V c(u)FCNC branching ratio to be smaller than about 36% [9] for V = γ or Z, so that in a pes-simistic scenario the OPAL efficiencies and cross-section limits quoted in Table 3 should berescaled by 64%.

The combination of all the data can be used to determine limits on the anomalouscoupling parameters κγ and κZ. First, the QCD and the ISR effects which modify the Born-level cross-section given in Equation 2 must be considered. The QCD correction is takenfrom Section 3 of Reference [36]; while the ISR correction is based on Reference [37]. Overall,the QCD and ISR corrections increase the Born-level cross-section by a constant factor ofabout 1.09 for all centre-of-mass energies and produce only a small distortion to the OPALexclusion region in the κγ − κZ plane.

The limits on the anomalous coupling parameters are obtained with the likelihood ratiomethod described in Reference [35]. Each centre-of-mass energy for the leptonic and thehadronic channel has been used as an independent channel. The variation of the selectionefficiencies for different top masses are taken from Table 3. Taking the statistical and sys-tematic errors into account the limit on the anomalous coupling parameters in the κγ − κZ

plane have been derived at the 95% CL. The reduction of the branching ratio BR(t → bW)due to possible FCNC decays derived at each point in the κγ −κZ plane is taken into accountin this generic FCNC production limit calculation. To compare our results with the limitsfrom CDF, exclusion regions for mt = 169, 174, and 179GeV/c2 in the κγ − κZ plane wereobtained. The results are shown in Figure 4. They correspond to upper limits of κγ <0.48and κZ <0.41 for a top quark mass of mt = 174GeV/c2, which becomes κγ <0.39 (0.60) andκZ <0.34 (0.52) for mt = 169 (179)GeV/c2. These exclusions translate into branching frac-tion limits of Br(t → Zc) + Br(t → Zu) < 9.7/13.7/20.6 % for mt = 169/174/179GeV/c2.All these results are consistent with recent results from the ALEPH Collaboration [38].

14

6 Summary

A search for single top quark production via FCNC has been performed with 600.1 pb−1 ofdata collected by OPAL in e+e− collision at

√s = 189 - 209GeV. In total, 85 events were

selected in the data with a SM expectation of 84.1 events. Limits on single top quark cross-sections have been derived at the 95% CL. This leads to model-dependent upper limitsof κγ <0.48 and κZ <0.41 for a top quark mass of mt = 174GeV/c2. The limits becomeκγ <0.39 (0.60) and κZ <0.34 (0.52) for mt = 169 (179)GeV/c2.

Acknowledgements:

We particularly wish to thank the SL Division for the efficient operation of the LEP acceler-ator at all energies and for their close cooperation with our experimental group. We thankour colleagues from CEA, DAPNIA/SPP, CE-Saclay for their efforts over the years on thetime-of-flight and trigger systems which we continue to use. In addition to the support staffat our own institutions we are pleased to acknowledge theDepartment of Energy, USA,National Science Foundation, USA,Particle Physics and Astronomy Research Council, UK,Natural Sciences and Engineering Research Council, Canada,Israel Science Foundation, administered by the Israel Academy of Science and Humanities,Minerva Gesellschaft,Benoziyo Center for High Energy Physics,Japanese Ministry of Education, Science and Culture (the Monbusho) and a grant under theMonbusho International Science Research Program,Japanese Society for the Promotion of Science (JSPS),German Israeli Bi-national Science Foundation (GIF),Bundesministerium fur Bildung und Forschung, Germany,National Research Council of Canada,Research Corporation, USA,Hungarian Foundation for Scientific Research, OTKA T-029328, T023793 and OTKA F-023259.

15

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17

OPAL

10-1

110

0 10 20 30 40 Ec(u) [GeV] e

ntri

es /

3 G

eV

10-1

110

20 40 60 80 100 Mqq

4C [GeV/c2] e

ntri

es /

7 G

eV/c

2

10-1

110

20 40 60 80 100 Mlν [GeV/c2]

ent

ries

/ 7

GeV

/c2

10-1

110

-6 -4 -2 ln y12

ent

ries

/ 0.

275

10-1

110

120 130 140 150 160 Mqq

6C + Mlν6C [GeV/c2]

ent

ries

/ 3

GeV

/c2

10-1

1

10

0 0.2 0.4 0.6 0.8 1 b-tag

ent

ries

/ 0.

05

10-11

10

0 0.2 0.4 0.6 0.8 1 P(b-tag,6C)

ent

ries

/ 0.

05 datasignal4fqq

Figure 1: Distributions of the likelihood variables for the leptonic channel at√

s ≃ 189GeV.Comparisons between the data, the SM 4-fermion (light grey), and qq backgrounds (grey)are shown. The dashed line represents single top MC events with mt = 174GeV/c2 and anarbitrary cross-section of σtop = 3pb.

18

OPAL

0

20

40

60

80

100

0 10 20 30 χ2

eve

nts/

2.5

0

25

50

75

100

0 0.05 0.1 0.15 0.2 Ec(u)/Evis

eve

nts/

0.01

2

0

20

40

60

80

0.6 0.7 0.8 0.9 1 Thrust

eve

nts/

0.02

0

50

100

150

0 0.2 0.4 0.6 0.8 1 b-tag

eve

nts/

0.05

0

50

100

-1 -0.5 0 cos(qq(W))

eve

nt/0

.1

data

signal

4f

qq

Figure 2: Distributions of the likelihood variables for the hadronic channel at√

s ≃ 189GeV.Comparisons between the data, the SM 4-fermion (light grey), and qq backgrounds (grey)are shown. The dashed line represents single top MC events with mt = 174GeV/c2 and anarbitrary cross-section of σtop = 3pb.

19

OPAL

1

10

10 2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Likelihood

ent

ries

/ 0.

04

data (a)signal4fqq

1

10

10 2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Likelihood

ent

ries

/ 0.

04

data (b)signal4fqq

Figure 3: Distributions of the likelihood variables for (a) the leptonic and (b) the hadronicchannels. The comparison between the data collected in 2000 at

√s ≃ 205GeV and

√s ≃

207GeV, the SM 4-fermion (light grey), and the qq backgrounds (grey) is shown. The dashedline represents single top MC events with mt = 174GeV/c2 and an arbitrary cross-sectionof σtop = 3pb.

20

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

OPAL

κγ

κ Z

excluded by CDF

excluded by OPAL

excluded by CDF

excluded by OPAL

mt=169 GeV/c2

mt=179 GeV/c2

Figure 4: The light grey region shows the OPAL exclusion region at 95% CL in the κZ − κγ

plane for mt = 174GeV/c2. The exclusion curves for different values of top quark massesare also shown. The hatched area shows the CDF exclusion region [9]. The OPAL limitsinclude QCD and ISR corrections to the Born-level cross-section defined in Equation 2.

21